12.540 Principles of the Global Positioning System

Lecture 08

Prof. Thomas Herring

Room 54-611; 253-5941

tah@mit.edu

http://geoweb.mit.edu/~tah/12.540

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Summary

• Review:– Examined methods for measuring distances– Examined GPS codes that allow a type of distance

measurement and phase to be measured

• Today:– Examine how the range measurements are defined

and used– Use of carrier phase measurements– Examine RINEX format and look at some “raw” data

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Pseudorange measurements

• When a GPS receiver measures the time offset it needs to apply to its replica of the code to reach maximum correlation with received signal, what is it measuring?

• It is measuring the time difference between when a signal was transmitted (based on satellite clock) and when it was received (based on receiver clock).

• If the satellite and receiver clocks were synchronized, this would be a measure of range

• Since they are not synchronized, it is called “pseudorange”

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Basic measurement types

• Pseudorange:

€

Pkp = (tk − t p ) ⋅c

Where Ppk is the pseudorange between receiver k and satellite

p; tk is the receiver clock time, tp is the satellite transmit time; and c is the speed of light

This expression can be related to the true range by introducing corrections to the clock times

€

tk = τ k + Δtk t p = τ p + Δt p

k and p are true times; tk and tp are clock corrections

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Basic measurement types

• Substituting into the equation of the pseudorange yields

• kp is true range, and the ionospheric and

atmospheric terms are introduced because the propagation velocity is not c.

€

Pkp = (τ k − τ p ) + (Δtk − Δt p )[ ] ⋅c

Pkp = ρ k

p + (Δtk − Δt p ) ⋅c + Ikp

Ionsphericdelay

{ + Akp

Atmosphericdelay

{

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Basic measurement types

• The equation for the pseudorange uses the true range and corrections applied for propagation delays because the propagation velocity is not the in-vacuum value, c, 2.99792458x108 m/s

• To convert times to distance c is used and then corrections applied for the actual velocity not equaling c. In RINEX data files, pseudorange is given in distance units.

• The true range is related to the positions of the ground receiver and satellite.

• Also need to account for noise in measurements

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Pseudorange noise

• Pseudorange noise (random and not so random errors in measurements) contributions:

– Correlation function width:The width of the correlation is

inversely proportional to the bandwidth of the signal.

Therefore the 1MHz bandwidth of C/A produces a peak 1

sec wide (300m) compared to the P(Y) code 10MHz

bandwidth which produces 0.1 sec peak (30 m)

Rough rule is that peak of correlation function can be

determined to 1% of width (with care). Therefore 3 m for C/A

code and 0.3 m for P(Y) code.

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Pseudorange noise

• More noise sources– Thermal noise: Effects of other random radio noise in the

GPS bandsBlack body radiation: I=2kT/2 where I is the specific intensity in, for example, watts/(m2Hz ster), k is Boltzman’s constant,1.380 x 10-23 watts/Hz/K and is wavelength.Depends on area of antenna, area of sky seen (ster=ster-radians), temperature T (Kelvin) and frequency. Since C/A code has narrower bandwidth, tracking it in theory has 10 times less thermal noise power (depends on tracking bandwidth) plus the factor of 2 more because of transmission power).Thermal noise is general smallest effect

– Multipath: Reflected signals (discussed later)

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Pseudorange noise

• The main noise sources are related to reflected signals and tracking approximations.

• High quality receiver: noise about 10 cm• Low cost receiver ($200): noise is a few meters

(depends on surroundings and antenna)• In general: C/A code pseudoranges are of similar

quality to P(Y) code ranges. C/A can use narrowband tracking which reduces amount of thermal noise

• Precise positioning (P-) code is not really the case.

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Phase measurements

• Carrier phase measurements are similar to pseudorange in that they are the difference in phase between the transmitting and receiving oscillators. Integration of the oscillator frequency gives the clock time.

• Basic notion in carrier phase: =ft where is phase and f is frequency

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Phase measurements

• The carrier phase is the difference between phase of receiver oscillator and signal received plus the number of cycles at the initial start of tracking

• The received phase is related to the transmitted phase and propagation time by

€

φkp (tr ) = φk (tr ) − φr

p (tr ) + Nkp (1)

€

φrp (tr ) = φt

p (tt ) = φtp (tr − ρ k

p /c) = φtp (tr ) − ˙ φ p (tr ) ⋅ρ k

p /c

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Phase measurements

• The rate of change of phase is frequency. Notice that the phase difference changes as /c changes. If clocks perfect and nothing moving then would be constant.

• Subtle effects in phase equation– Phase received at time t = phase transmitted at t- (riding the wave)

– Transmitter phase referred to ground time (used later). Also possible to formulate as transmit time.

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Phase measurements

• When phase is used it is converted to distance using the standard L1 and L2 frequencies and vacuum speed of light.

• Clock terms are introduced to account for difference between true frequencies and nominal frequencies. As with range ionospheric and atmospheric delays account for propagation velocity

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Precision of phase measurements

• Nominally phase can be measured to 1% of wavelength (~2mm L1 and ~2.4 mm L2)

• Again effected by multipath, ionospheric delays (~30m), atmospheric delays (3-30m).

• Since phase is more precise than range, more effects need to be carefully accounted for with phase.

• Precise and consistent definition of time of events is one the most critical areas

• In general, phase can be treated like range measurement with unknown offset due to cycles and offsets of oscillator phases.

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GPS Data file formats

• Receivers use there own propriety (binary) formats but programs convert these to standard format called Receiver Independent Exchange Format (RINEX)

• teqc available at http://www.unavco.org/facility/software/teqc/teqc.html is one of the most common

• The link to the RINEX format is:• ftp://igscb.jpl.nasa.gov/igscb/data/format/rinex2.txt

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Rinex header

2.00 OBSERVATION DATA G (GPS) RINEX VERSION / TYPEteqc 1998Jul1 Thomas Herring 20020117 06:28:28UTCPGM / RUN BY / DATELinux 2.0.30|PentPro|gcc|Linux|486/DX+ COMMENTBIT 2 OF LLI FLAGS DATA COLLECTED UNDER A/S CONDITION COMMENTETAB MARKER NAMEtah MIT OBSERVER / AGENCY7910 TRIMBLE 4000SSE NP 7.19; SP 3.04 REC # / TYPE / VERS7910 TRM22020.00+GP ANT # / TYPE -2225431.6719 -4676995.2141 3711599.9580 APPROX POSITION XYZ 1.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N 1 1 WAVELENGTH FACT L1/2 7 L1 L2 C1 P2 P1 D1 D2 # / TYPES OF OBSERV 15.0000 INTERVAL SNR is mapped to RINEX snr flag value [1-9] COMMENT L1: 3 -> 1; 8 -> 5; 40 -> 9 COMMENT L2: 1 -> 1; 5 -> 5; 60 -> 9 COMMENT 2002 1 16 18 49 15.000000 TIME OF FIRST OBS END OF HEADER

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RINEX Data block

2 1 16 18 49 15.0000000 0 6G 2G 7G11G26G27G28

787986.44256 602246.12855 23296205.6024 23296215.6954

-1344.9694 -1048.0284

-2277471.81757 -1740781.13556 21398430.3444 21398436.5904

2700.6094 2104.3714

-1100283.16556 -822375.51955 23502290.7894 23502300.4844

1062.9224 828.2514

-1925082.16955 -1445658.56955 23293616.9844 23293626.4574

2176.8284 1696.2304

1016475.79056 786021.95356 21979554.0634 21979561.0984

-1782.8124 -1389.2054

-572573.66057 -446158.58357 20873925.7664 20873929.7624

446.3594 347.8134

2 1 16 18 49 30.0000000 0 6G 2G 7G11G26G27G28

• Phase in cycles, range in meters

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Examine Rinex file data

• Next set of plots will look at the contents of a rinex file.

• Examples for one satellite over about 1 hour interval:– Raw range data– Raw phase data– Differences between data

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Raw range data

23200000

23400000

23600000

23800000

24000000

24200000

24400000

24600000

18.8 19.0 19.2 19.4 19.6 19.8

C1_range P2_range

C1_range (m)

Hrs

Drop out

Bad measurement

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Raw phase data (Note: sign)

-2000000

0

2000000

4000000

6000000

8000000

18.8 19.0 19.2 19.4 19.6 19.8

L1_phase L2_phase

Phase (cycles)

Hrs

Cycle slip at L2

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L2-L1 range differences

5

10

15

20

25

30

18.8 19.0 19.2 19.4 19.6 19.8

2- 1 ( )P C m

2- 1 ( )P C m

Hrs

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L2-L1 phase differences

-5000

0

5000

10000

15000

20000

18.8 19.0 19.2 19.4 19.6 19.8

2*L 2- 1*L

1 ( )m

2*L

2- 1*L

1 ( )m

Hrs

Cycle slip repaired approximately

-Notice time to re lock

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Zoomed L2-L1 phase

-20

-15

-10

-5

0

5

18.8 19.0 19.2 19.4 19.6 19.8

2*L 2- 1*L

1 ( )m

2*L

2- 1*L

1 ( )m

Hrs

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Plot characteristics

• Data set plotted etab.plt.dat• Notice phase difference is opposite sign to

range difference (discuss more in propagation lectures)

• More manipulation can me made of data: How about C1-L1*

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Summary

• Looked at definitions of data types• Looked at data and its characteristics.• Next class, we finish observables and will

examine:– Combination of range and phase that tell us more

things– How well with a simple model can we match the

data shown.– Where do you get GPS data?